7. (a) Prove that $$\frac { \mathrm { d } } { \mathrm {~d} x } \left( a ^ { x } \right) = a ^ { x } \ln a .$$ A curve has the equation \(y = 4 ^ { x } - 2 ^ { x - 1 } + 1\).
(b) Show that the tangent to the curve at the point where it crosses the \(y\)-axis has the equation $$3 x \ln 2 - 2 y + 3 = 0 .$$ (c) Find the exact coordinates of the stationary point of the curve.
7. continued